Answered: Plane II is spanned by the vectors: -…

Plane II is spanned by the vectors: - (2) · P² - (4) P1=2 P21 3 Subspace W is spanned by the vectors: 2 W1 - (9) · 1 W2 1 = (³)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 9E

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Question

You are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by two
vectors, w1 and w2. Your task is to project the plane Π onto the subspace W.
First, answer the question of what the projection matrix is that projects onto the subspace W and how to
apply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidt
method to find an orthonormal basis for subspace W, before then using the resulting basis vectors for the
projection. Last, compare the results obtained from both methods

Plane II is spanned by the vectors:
- (2) · P² - (4)
P1=2
P21
3
Subspace W is spanned by the vectors:
2
W1
- (9) ·
1
W2
1
= (³)

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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